19920009925
DESCRIPTION
pultrusionTRANSCRIPT
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FINAL REPORT
PULTRUSION PROCESS CHARACTERIZATION
NASA Contract NAS8-37193
Submitted by
James G. Vaughan and Robert M. Hackett
School of Engineering
The University of Mississippi
University, MS 38677
(NASA-CR-184275) PULTRUSION PROCESS N92-19167CHARACTERIZATION Final Report, 7 Aug. 1990 -6 Aug. 1991 (Mississippi Univ.) 127 p
CSCL 13H UnclasG3/31 00714-22
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TABLE OF CONTENTS
PageNumber
Pultrusion Process Characterization
Introduction 1Process Description 2
Section I: Experimental Characterization of the Pultrusion Process
Experimental Design Characterization Methods 1Experimental Procedure 6Results and Discussion 9Summary 30References 31
Section II: Two-Dimensional Finite Element Modeling of the Pultrusion ofFiber/Thermosetting Resin Composite Materials
Introduction 1Heat Transfer Model 5Curing Process Model 11Formulation of the Degree-of-Cure Model and Calculation Technique 35Numerical Solution and Discussion 37References . . . 46Appendix 49
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LIST OF TABLES
PageNumber
Section I: Experimental Characterization of the Pultrusion Process
Table I. Central Composite Experimental Test Plan (Standard Order) 4
Table II. Central Composite Experimental Test Plan (Random Order) 5
Table III. Formulation Table for the Shell EPON 9420 Epoxy System 7
Table IV. Range of Pultrusion Process Parameters forCentral Composite Design Experiments 8
Table V. Pull Load for the 32 Pultrusion Experiments 13
Table VI. Flexural Strength of Pultrusion Test Samples 21
Table VII. Short-Beam Shear Strength - Room Temperature 22
Table VIII. Short-Beam Shear Strength - High Temperature (350 F) 23
Table IX. Coefficients for Experimental Model - Complete Model 24
Table X. Coefficients for Experimental Model - Reduced Set 25
11
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LIST OF FIGURES
PageNumber
Section I: Experimental Characterization of the Pultrusion Process
Figure 1. Thermocouple Profiles of Four Die Temperature Extremes 11
Figure 2. Measured Viscosity of Shell EPON 9420/9370/537 Epoxy Systemat Start and Finish of the 32 Characterization Experiments 12
Figure 3. Typical Test Measurements for Flexural Strength Samples 16
Figure 4. Typical Test Measurements for Short-Beam Shear Strength Samples . . 17
Figure 5. Maximum-Minimum-Average Bar Chart of Flexural Strength- ASTM D790 Method II . . 18
Figure 6. Maximum-Minimum-Average Bar Chart of Short-Beam ShearStrength (Room Temperature) - ASTM D2344 19
Figure 7. Maximum-Minimum-Average Bar Chart of Short-Beam ShearStrength (High Temperature - 350 F) - ASTM D2344 20
Figure 8. A comparison of flexural strengths predicted by the completeexperimental model and a reduced set model to the measuredflexural strengths 26
Figure 9. A comparison of short-beam shear strengths predicted by the completeexperimental model and a reduced set model to the measured roomtemperature short-beam shear strengths 27
Figure 10. A comparison of short-beam shear strengths predicted by the completeexperimental model and a reduced set model to the measured hightemperature (350 F) short-beam shear strengths 28
in
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LIST OF FIGURESPage
Number
Section II: Two-Dimensional Finite Element Modeling of the Pultrusion ofFiber/Thermosetting Resin Composite Materials
Figure 1. Schematic Diagram of the Pultrusion Process 2
Figure 2. Coordinates of Die with Rectangular Cross Section 7
Figure 3. Notation for Interior Element Boundary Flux Integral 18
Figure 4. Element Local Coordinates 23
Figure 5, Axisymmetric Configuration of Isoparametric Element with Four Nodes 29
Figure 6, Temperature Profile of the Material 38
Figure 7. Temperature Profile Solved with Convective Boundary Conditions . . . . 39
Figure 8, Temperature Profile Solved with Adjusted Boundary Conditions 41Figure 9, Profile of the Degree-of-Cure of the Material 42
Figure 10. Temperature Profile of the One-Dimensional Model 45
IV
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PULTRUSION PROCESS CHARACTERIZATION
INTRODUCTION
Pultrusion is a process through which high-modulus, lightweight composite structural7
members such as beams, truss components, stiffeners, etc., are manufactured. The basic
operation, simple in concept - complex in detail, consists of pulling high-strength high-\
modulus reinforcement fibers/matvthrough a thermosetting resin bath, and then through a
heated die where the wetted fiber bundle cures, thus producing a structurally sound part
exiting the die. In the case of the pultrusion of thermoplastic composites, the material
enters the die in the form of impregnated rovings and is consolidated. During the pultrusion
of thermosetting resin composites major processMnteractions occur between the chemicalreaction occurring during "cure" inside the die, the die temperature profile, and the pull
\speed of the reinforcement. \
" ~-\The pultrusion process, though a well-developed processing art, lacks a fundamental
scientific understanding. The objective of the present.. study was to determine, bothexperimentally and analytically, the process parameters most important in characterizing and
optimizing the pultrusion of uniaxial fibers. The effects of process parameter interactions
were experimentally examined as a function of the pultruded product properties. A
numerical description based on these experimental results was developed. This work was
1 lead by Dr. James Vaughan. An. analytical model of the pultrusion process was also
-
developed; this work was lead by Dr. Robert Hackett. The objective of the modeling effortwas the formulation of a two-dimensional heat transfer model and developing of solutions
for the governing differential equations using the finite element method.
PROCESS DESCRIPTION
In the pultrusion of thermosetting resin composites reinforcing material is assembled
and oriented to enter the die in the configuration necessary for the development of the
desired mechanical properties of the produced structural member. Heat is supplied to the
process by electrically heated metal platens. Cooling water at the die entrance controls the
transition from ambient to the die temperature. Hydraulic pullers provide a continuous
movement of the product. A chemical reaction process occurs within the die and is initiated
by the application of heat to the chemically active resin. The reaction progresses while
under the influence of pressure within the die. It is exothermic, and at some position within
the die the relationship of heat flux is inverted and the degree of cure progresses to the
point where shrinkage allows the part to release from the die wall.
Precise control of the thermal and chemical phenomena occurring within the die is
of utmost importance. If the reaction proceeds too rapidly the composite can bond to the
die surface. This results in a loss of production, a low-quality product, and possible damage
to the die. Once the process is in progress, the pulling force must be regulated to ensure
that the line speed does not vary, since speed fluctuations translate directly into variations
in cure conditions.
Outwardly the process is deceptively simple in that the function is well-understood.
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However, without an in-depth knowledge of the interaction of the various system variables,
one cannot achieve efficient performance of the process. Essentially, only general qualitative
information about what occurs inside the pultrusion die is presently available. In the liquid
zone of the process, the temperature of the die exceeds that of the resin with the
temperature of both increasing. Within the gel zone the peak exotherm of the resin is
reached, usually being well above the temperature of the die. In effect, over the remainder
of the process the die is drawing heat from the curing composite, thereby reducing thermal
shock to the product upon its exit from the die. The material traveling through the process
undergoes a number of dynamic changes as a result of the temperature
environment within the die. The nature of these changes is manifested, to an extent,
through the variation of the viscosity of the resin over the length of the die. Over the initial
portion, the viscosity decreases as the temperature of the material increases through
conduction. This reduction aids in the continuing wet-out of any unsaturated fibers. At the
point at which the chemical reaction is initiated, the change in viscosity is reversed, and the
viscosity rapidly increases through the stages of gelation and final cure. It is desirable for
this reaction to occur under sufficient pressure to ensure composite integrity and to minimize
internal porosity which can occur from vapor pressures within the reacting material.
The pressure at the material-die interface is a measurement of normal surface forces
which, combined with the appropriate coefficients of friction, yield a measurement of
frictional force, or resistance to pull. Pressures can be associated with the viscosity of the
resin, the volumetric ratios of fiber and resin, the coefficient of thermal expansion of the
materials, the cross-sectional geometry of the cavity, the length of die over which there is
-
material contact, the coefficients of friction of the die with respect to the liquid, gel and
solid, and the degree of shrinkage of the solid. The efficiency of the process can be greatly
enhanced through a better understanding of the pressure distribution.
The purpose of this introductory description has been to define the pultrusion process
with respect to thermosetting resin systems, highlight the most important process variables,
indicate the complex interdependence among these variables which renders an intuitive grasp
of the process almost impossible to attain, and thus, emphasize the need for definition of
process variable interactions in order to gain insight into the process.
The remainder of this report will be broken into two sections to discuss the work
completed to better characterize the pultrusion process. Section 1 will deal with the
experimental work performed to statistically characterize pultrusion. This work was directed
by Dr. James G. Vaughan. Section II will present the finite element modeling studies
conducted by Dr. Robert M. Hackett.
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SECTION I
EXPERIMENTAL CHARACTERIZATION
OF THE PULTRUSION PROCESS
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EXPERIMENTAL CHARACTERIZATION
OF THE PULTRUSION PROCESS
EXPERIMENTAL DESIGN OPTIMIZATION METHODS
An optimum process control - product performance ratio for the pultrusion process
can only be achieved through a basic understanding and control of all the variables that
influence the quality of the final product. To accomplish this objective, considerable timewas spent in planning an experimental study to obtain the needed understanding. The
experimental procedure had to be capable of determining all process control variables of
importance, yet constrained due to the fact that the time for experimentation would be
limited. The procedure had to take into account the fact that many of the process variables
may interact in their overall effect on the product in a manner called "negative interaction".
Negative interaction implies that at one process setting, an increase in a given control
variable setting causes an increase in a measured product yield, but at another setting of a
different variable, an increase in the first variable now causes a decrease in the product
yield.
Reviewing standard plans of experimentation, it was apparent that classical one-
factor-at-a-time experiments would not be useful. The classical concept of changing only one
factor at a time to determine its effect on product yield cannot deal with interaction among
variables, nor is there an accurate method of estimating experimental error. These factors
1
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are known to be present in the pultrusion process. Also, the classical technique requires a
great deal of experimental time with little understanding gained to show for the effort. Thus
a better experimentation strategy was required.
The second broad class of experimental strategy used by engineers and scientists deals
with statistical experimentation. Two major subdivisions of statistical experiments are thefull factorial and the fractional or "incomplete" factorial approaches. Examination of the
various statistically based experimental plans indicated that too many variables were
probably of importance in the pultrusion process to use a full factorial experiment. In
looking at various fractional factorial experiments suitable for fitting response surfaces, the
central composite design technique [1] and the Box-Behnken method [2] are cited the most
often. Both of these experimental designs are fractions of the 3k factorials, but only require
enough observations to estimate main and second-order interactions. Main factors are the
process parameters themselves while second-order interactions are the interactions of one
main process parameter with another main process parameter. For this study the central
composite design showed the greatest possible benefit considering the number of possible
pultrusion variables. For five process parameters of interest, the central composite design
requires 32 experiments for analysis of all interactions up to second-order, whereas the Box-
Behnken technique would require 47 experiments for similar analysis.
The central composite design for five process parameters consists of 16 multi-variable
experiments, three mid-point experiments, and 13 star point experiments. These 32
experiments allow all main and two factor interactions to be determined without confounding
for five process parameters. Thus the method allows the determination of the importance
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of each process parameter, separately and in combination with each other process
parameter. The experimental plan for the 32 experiments is listed in Table I. The plan in
Table I is listed in standard statistical design order while the plan shown in Table II is listed
in the random order as run.
In Tables I and II, the symbols "-2" and "+2" represent the lowest and highest
normalized levels of the 5 factors, while "0" represents the center point of each factor range.
The symbols "-1" and "1" are halfway between the "0" and "2" points. The first 16
experiments constitute a 25'1 resolution IV experiment. The last series of experiments as
listed in Table I and II are the star point experiments. Statistical tests can be performed to
verify that the variance in the experimental data is actually due to interactions and not to
experimental error. The order in which these trials are run is randomized to eliminate
systematic variation or bias in the experiment.
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TABLE ICentral Composite Experimental Test Plan
Listed in Standard Experimental Order
RandomTest #
161
11175
10121882796
14151334
1922203024272331292126282532
TestPlan#
123456789
1011121314151617181920212223242526272829303132
Normalized Test Parameters1
-11
-1 1-11
-11
-11
-11
-11
-11000000
-2000020000
2
-1-111
-1-111
-1-111
-1-1110000000
-200002000
3
-1-1-1-11111
-1-1-1-1111100000000
-20000200
4
-1-1-1-1-1-1-1-111111111000000000
-2000020
5
1-1-11
-111
-i-iii
-ii
-i-ii0000000000
-200002
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TABLE IICentral Composite Experimental Test Plan
Listed in Random Experimental Order
RandomTest#
123456789
1011121314151617181920212223242526272829303132
TestPlan#
21017185
13119
12637
161415148
1921282025233129243027222632
Normalized Test Parameters1
1100
-1-1-1-111
-1-111
-1-11100200
-200000000
2
-1-100
-1-11
-11
-1111
-11
-11100000002
-200000
3
-1-10011
-1-1-11
-11111
-1-110000
-2000020000
4
-1100
-11111
-1-1-1111
-1-1-1000000200000
-20
5
-1100
-111
-1-11
-111
-1-111
-10000000000
-2002
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EXPERIMENTAL PROCEDURE
The composite system chosen for study was the Shell EPON 9420/9470/537 epoxy
system with graphite fiber. The polyacrylonitrile (PAN) base graphite fiber, type I AS4-
W-12K, was manufactured by Hercules Inc. A formulation for the epoxy system is given in
Table III. The epoxy resin was mixed daily for each series of experiments and held at
approximately 70-75 F before being placed into the pultrusion resin bath. The pultruded
product shape was a 1 x 1/8 inch rectangle.
Considerable time was spent in readying the NASA/MSFC pultruder for the
experiments required for the statistical optimization trials. New rubber grips were obtained
to better grip the graphite fibers for initial pulling through the die. New alignment blocks,
for preparing the fibers into the proper shape before entering the die, were machined.
Methods of running the fibers through the resin bath for maximum wet-out were examined.
From prove-in experiments, five operating parameters were considered most
important for optimization of the pultrusion process. These five parameters were the die
platen heating temperatures (zone 1 and zone 2), the percent fiber content in the pultruded
product, the pull speed of the product, and the amount of clay filler in the epoxy. Prove-in
experiments, along with the Shell literature for the EPON 9420 epoxy, had indicated that
the platen temperature should reach 400 F (204 C). Previous experiments had indicated
that fiber percentages (by volume) less than 59% would result in an under-developed
product shape and amounts greater than 65% were not possible for continuous pulling at
high speeds. Thus the control parameters, with their various operating extremes, were
selected for the optimization experiments as shown in Table IV.
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TABLE IIIFormulation Table for the Shell EPON 9420 Epoxy System
phr
A. EPON 9420 resin 100EPON 537 accelerator 2.0AXEL INT 18-46 (internal release agent) 0.65
B. ASP 400-P (clay filler) 20
C EPON 9470 curing agent 24.4
Mix all components of A. together for one minute. Add component B. to above andmix until homogenous (app. 5 minutes). Do not allow mix to heat due to mixingaction. Add component C. and mix for no more than 2 to 3 minutes. Again allowno heat to be generated.
EPON is a registered trademark of Shell Chemical Company.AXEL is a trademark of Axel Plastics Research Laboratories.ASP 400-P is a product of Engelhard Minerals & Chemicals Corporation.
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TABLE IV
Range of Pultrusion Process Parametersfor Central Composite Design Experiments
Process Parameter Test Range
- 2 - 1 0 1 2
Process Parameter 1: Filler (phr) 16 17 18 19 20Process Parameter 2: Graphite tows 101 103 105 107 109
% 59.7 60.9 62.1 63.3 64.4
Process Parameter 3: Pull Speed in/min 8 10 12 14 16
Process Parameter 4: Zone 1 Temp (F) 350 360 370 380 390Process Parameter 5: Zone 2 Temp (F) 350 360 370 380 390
8
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RESULTS AND DISCUSSION
Figure 1 shows internal processing temperature profiles of the die for four platen
control point temperatures. The control set point temperatures for each of the four profiles
is noted in the Figure legend. The four plotted profiles represent the four temperature
extremes from the range of zone temperature settings listed in Table IV. As can be seen
from the plotted data, the peak temperature inside the die is approximately 40 F higher than
the die set point temperature. Part of the reason for this overshoot lies with the two
thermocouples in each heating platen that are used to control the die temperature to the
set point temperature. These two control thermocouples, for both the bottom and top
heating platen, are located 10.3 inches and 24.9 inches from the platen edge at the die
entrance. Due to the placement of the cartridge heating rods within the heating platens, the
sensing thermocouples can not determine the heat build-up between the two heating zones.
Thus the platens heat to the set point temperature as designed, but overshoot the set point
temperature in the region between the two zone control thermocouples. Another reason
for the overshoot is the heat released due to the epoxy cure exotherm. Temperature profile
tests indicate that the curing of the epoxy generates an additional 10 to 20 F to the peak
temperature.
The temperature profile is not centered at the middle of the heated die. In fact, the
peak temperature of all four profiles is in a different die location. Water cooling was used
to prevent rapid heat build-up in the entrance section of the die. This has an effect of
keeping the entrance portion of the die cooler than the remaining areas. As product is
pulled through the die, heat tends to be carried toward the exit end of the die thus making
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this region hotter than the other regions. Even though the heated platen length is only 36
inches and the die only 30 inches, the temperature within the pultruded product remains
high for quite some distance outside the die as can be seen in Figure 1.
In Figure 1 it can also be observed that the temperature profiles with zone 1 high exit
the die at a lower temperature than when zone 1 is low and zone 2 is high. This is due to
the location of the epoxy exotherm within the die. When zone 1 is held at a high
temperature, the resin exotherm tends to occur much earlier in the die. Thus much heat is
released in the front portion of the die and little heat is produced in the rear of the die.
However, when the front of the die is kept cooler and the zone 2 is high, then the resin
exotherms in the rear of the die keeping the back portion of the die hot. This is why the
"L-H" temperature profile appears to hold a higher temperature longer than any of the other
three profiles.
Viscosity measurements were made for all resin batches used in the 32 experiments.
These viscosity measurements are shown in Figure 2. Many of the first experiments used
the same resin mix so the viscosity measurements are plotted as the same value for these
first experiments. Towards the end of the experimentation, viscosity measurements were
also made on the resin at the end of the experiment. These final viscosity readings are also
shown in Figure 2 for experiments 23 - 32. As can be seen, an increase in viscosity of
approximately 1000 cps during the course of the experiment was typical.
Table V presents the range of pull pressures observed during the pultrusion of the
32 test experiments. These values were taken from the Pultrusion Technology, Inc. (PTI)
readout on the main display panel which uses the hydraulic load on the puller to determine
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TABLE V
Pull Load for the 32 Pultrusion Experiments
Experiment Number Pull Load (Ibs)1 Not Recorded2 Not Recorded3 1200 - 17004 1200 - 17005 4300 - 35006 6000 - 14007 2000 - 30008 3000 - 50009 3500 - 760010 8000 - 625011 2900 - 400012 5250 - 600013 7000 - 250014 2400 - 500015 2250 - 450016 100017 7600 - 900018 1000019 2250 - 500020 2250 - 800021 120022 3750-610023 2000 - 100024 120025 2300 - 400026 275027 130028 3500 - 550029 150030 3300 - 150031 120032 3100 - 2400
13
-
pull load. As can be seen from the data in Table V a large variation in pull pressure
occurred from these experiments. Where the pull pressure varied greatly within one run,.1
the range of pull pressure observed is noted. If only one value is given for the pull pressure,
then it was observed that the pull pressure did not vary by more than Hh 200 pounds.
Fifty feet of 1 x 1/8 inch product were run for each pultrusion experiment. Ten
sections, each five feet long were cut and labeled from the 50 feet of product. After all the
pultrusion characterization experiments were completed, the following measurements were
made on the 32 sets of pultruded product. Mechanical property tests were conducted for
flexural shear strength (ASTM D790 Method II), and short-beam shear strength (ASTMD2344). Tensile strength - modulus (ASTM D3039) were also going to be conducted, but
due to a delay in testing of the tensile samples, these data can not be included in this report.
All tests were conducted at room temperature (approximately 75-85 F (24-30 C) except for
the short-beam shear test which was conducted both at room temperature and at 350 F (177
C). Material samples for each test were selected from product produced every 10 feet of
each experiment to determine if a major change in the process/property occurred during thetime of the test. No change was observed.
Typical test results for the flexural shear tests are shown in Figure 3. In Figure 3 are
plotted the flexural load versus the flexural displacement. The loading rate was 0.2 in/min.
The data shown are for the five test samples of experiment 8, although similar curves were
observed for all 32 experiments. Typical test results for the room temperature short-beam
shear tests are shown in Figure 4; the high temperature (350 F) short-beam shear results are
similar except for lower breaking stresses. The loading rate for the short-beam shear tests
14
-
was 0.05 in/min.
The data for all of the flexural test results are given in Figure 5. In Figure 5 the data
are presented in the form of a maximum - minimum bar chart with the average of the tests
results shown as a tick mark on the bar. Data for all 32 experiments are shown. A similar
type of bar chart for the room temperature short-beam shear tests is shown in Figure 6 and
the high temperature short-beam shear results in Figure 7.
All of the mechanical property test data, with averages and standard deviations, are
given in Tables VI-VIII. As can be seen from Figures 5-7 and the data in Tables VI-VIII
a large variation in test properties were observed. However, a simple examination of these
data do not indicate any given pattern variation with regard to the five process parameters
under investigation.
To further examine the effects of the pultrusion process parameters, a standard
central composite design analysis was conducted. For these analyses, each of the average
mechanical property values for each of the 32 experiments were used to determine a second
order equation as a model of the pultrusion process. In these analyses all experimental runs
were used with equal weight given to all equation coefficients. Table IX lists the coefficients
for the experimental model. In Table IX it can be seen that many of the coefficients are
not of major importance. By eliminating those coefficients of minor value and performingthe fit analysis for those terms that produce a major influence in the experimental model,a reduced set of new fit coefficients can be developed. These reduced sets of equation
coefficients are given in Table X for flexural strength, room temperature short-beam shear
strength, and high temperature (350 F) short-beam shear strength. The R squared values
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TABLE VIFlexural Strength of Pultrusion Test Samples (ksi)
RandomTest #
123456789
1011121314151617181920212223242526272829303132
Individual Product Samples1
233.9235.7198.9225.8230.2220.4231.0217.2207.7225.0218.8224.6189.9
_
218.0195.0226.7222.7223.1
-
224.5_
210.5220.4218.9205.6214.9218.6195.1210.0220.7224.0
2
239.1242.9216.8234.8217.7174.2199.9228.0235.4232.8236.9234.8216.2224.2218.0222.2208.0
_
-
_
227.1217.0227.8207.0225.9216.3199.0212.1201.6222.4224.2207.8
3
206.9214.5219.9202.6224.1193.4227.9210.0235.0218.7234.0225.0229.8225.0227.2210.1226.4198.4
-
228.1223.0228.1225.7210.3223.3223.9207.4203.0208.5220.6219.4198.5
4
235.0220.6235.1231.4195.1206.8239.8209.7228.3175.9237.5195.3229.4228.5222.0220.7223.3213.4218.9230.0223.0222.5216.7214.2219.4228.4208.8216.8203.3217.2194.8208.8
5 STD.DEV.
204.5209.7218.6212.8211.3207.0192.5224.1220.1221.1223.3190.9234.7231.2185.5220.6231.6218.6230.5
1.33224.1211.2219.7220.3220.7222.3215.8208.1212.1
.
212.8228.1
16.7314.1012.8413.5013.5117.4820.748.22
11.6522.338.51
19.6718.183.24
16.4511.549.01
10.665.90
229.01.667.276.985.962.958.836.756.366.555.48
11.6812.27
AVG.
223.9224.7217.8221.5215.7200.4218.2217.8225.3214.7230.1214.1220.0227.2214.2213.7223.2213.3224.2
224.3219.7220.1214.4221.6219.3209.2211.7204.1217.6214.4213.4
21
-
TABLE VIIShort-Beam Shear Strength (psi) - Room Temperature
RandomTest #
123456789
1011121314151617181920212223242526272829303132
Individual Product Samples1
11,11111,62310,37211,91611,34612,15511,26311,90911,36911,80810,53311,36811,45410,69010,71610,89712,02812,21811,17412,10410,1449,087
11,58011,34811,42310,06111,58511,21810,07710,92911,16711,648
2
9,61712,29710,29511,39711,1548,942
11,26811,71211,52711,56511,43411,93511,91511,69611,95111,69312,10811,98611,30812,23810,90310,68312,15011,74612,25610,94812,20411,69210,91511,44111,32211,897
3
10,52311,80612,58111,89711,56811,49211,55111,56311,84211,68011,74411,70211,46411,70911,05811,88412,28311,93111,49112,19311,16411,68511,95511,31712,11811,88112,15511,74811,11211,58711,39112,413
4
10,53912,01510,99011,84111,419
-
12,08711,76911,74811,75311,74711,72811,74211,74911,93611,54612,44012,08011,83712,22811,50911,68211,79211,99212,29312,30711,95511,92411,19811,72811,28812,214
5
10,17612,04411,71411,77911,402
-
12,06111,63211,68611,69811,38511,79911,72111,80110,69011,77012,38712,18312,15512,1269,385
11,70111,99712,13412,09912,19811,90012,16011,51811,46411,21712,240
STD.DEV.
548255964213150
1,69640813318891
497210198471632390177123401
60854
1,13821736935495624634854230288
306
AVG.
10,39311,95711,19011,76611,37810,86311,64611,71711,63411,70111,36911,70611,65911,52911,27011,55812,24912,08011,59312,17810,62110,96711,89511,70812,03811,47911,96011,74810,96411,43011,27712,082
22
-
TABLE VIIIShort-Beam Shear Strength (psi) - High Temperature (350F)
RandomTest#
123456789
1011121314151617181920212223242526272829303132
Individual Product Samples1
2,2512,4912,2002,3512,9652,3982,7442,3972,2642,4192,4742,5752,6092,5542,2702,4272,9062,9072,5592,7462,3742,0442,5622,3442,3672,3992,2482,2233,2612,1473,4152,483
2
2,0862,5392,0592,1971,9271,9912,3692,3672,4782,4892,4242,5392,7132,4542,3182,5382,8832,7042,6442,7122,4792,2732,7252,2472,3712,6412,4382,0892,0192,2882,0662,312
3
2,2852,7412,4772,1272,1112,1572,5362,2812,5242,3692,4352,7042,8522,4722,3742,4332,8652,5302,5712,8592,5272,5302,5332,2362,3812,5802,4622,0962,1002,1972,1032,472
4
2,2322,4092,3142,4372,274
-
2,5922,2722,4602,2732,4712,5562,5102,4282,1412,3673,0132,4842,6862,8582,4472,4562,5652,2912,4132,7052,4913,2742,1342,2512,0442,542
5
3,3852,5142,2952,2231,959
-
2,4722,2702,4242,3442,4492,3902,6292,7582,1982,3412,7782,5422,7142,7582,3902,4932,4972,3762,4122,6032,1482,3552,1152,4532,1282,662
STD.DEV.
52912315412542420514060
1008122
112128134937685
174696863
202886022
114151497525117596127
AVG.
2,4482,5392,2692,2672,2472,1822,5432,3172,4302,3792,4512,5532,6622,5332,2602,4212,8892,6332,6352,7872,4442,3592,5772,2992,3892,5862,3572,4072,3262,2672,3512,494
23
-
TABLE IXCoefficients for Experimental Mathematical Model
Complete Model
Equation Flexural Short-Beam Short-BeamCoefficients Stress (ksi) Shear Stress (psi) Shear Stress (psi)
350 F
b(0) 220.75 11529.22 2422.15b(a) 2.83 -19.96 76.21b(b) 1.69 64.79 75.54b(c) -3.09 -26.29 -38.71b(d) 0.56 56.79 -19.96b(e) -0.83 175.21 49.38b(aa) 0.32 -97.59 -6.27b(bb) -0.96 41.16 18.73b(cc) -0.55 66.66 23.85b(dd) -0.02 25.66 -6.65b(ee) -2.33 -7.97 3.35b(ab) -2.36 97.94 4.69b(ac) 0.84 113.06 24.44b(ad) 2.82 54.44 11.56b(ae) 1.52 118.19 0.06b(bc) -0.82 -1.81 11.19b(bd) -0.32 -139.44 -44.19b(be) 1.48 -9.69 56.06b(cd) 0.56 -183.06 12.81b(ce) -0.24 -164.06 -40.19b(de) -0.24 -126.19 -4.81
a = > process parameter 1 = amount of filler (phr)b = > process parameter 2 = percent of graphite (%)c = > process parameter 3 = pull speed (in/min)d = > process parameter 4 = zone 1 die temperature (F)e = > process parameter 5 = zone 2 die temperature (F)
24
-
TABLE XCoefficients for Experimental Mathematical Model
Reduced Set
EquationCoefficients
b(0)b(a)b(b)b(c)b(d)b(e)b(aa)b(bb)b(cc)b(dd)b(ee)b(ab)b(ac)b(ad)b(ae)b(bc)b(bd)b(be)b(cd)b(ce)b(de)R square
FlexuralStress (ksi)
220.303.672.42
-2.25
-1.67
Short-Beam Short-BeamShear Stress (psi) Shear Stress (psi)
350 F
11550.16 2446.9176.2175.54
-38.71
175.21
-2.15
2.13
56.06
0.54
a => process parameter 1b = > process parameter 2c = > process parameter 3d = > process parameter 4e = > process parameter 5
-183.06-164.06
0.28
amount of filler (phr)percent of graphite (%)pull speed (in/min)zone 1 die temperature (F)zone 2 die temperature (F)
0.51
25
-
CDCO
CDO13
T3CD
OC
CDT3O
CO
5
OS4-*O
T)203
rt"uOOE
13E(U
'S
T3U
a2a.M
I
U J3
t4-i ao ga iso
-
r^ -^Q.
CDH_E
-
0).Q
CO
I-CO
iCDQ
CO
CM cvi
CDCO
CDO
CDDC
CD
OSCD
"a.EoO
tCTJ
1
u
ac03
13-aoS"3u
,"T3
-
values are also given relating the quality of the fit. From the R squared values it can be
seen that the room temperature short-beam strength have little statistical significance and
thus they will not be discussed any further. The R squared values for flexural and high
temperature short-beam shear, although not as high as one would like, can be considered
for limited predictive cases. Figures 8-10 show the fit of the predictive model to the actual
measured mechanical properties of flexural strength, room temperature short-beam shear
strength, and high temperature (350 F) short-beam shear strength. Shown are the fit datafor the complete model and the reduced set model. As can be seen, there are some trade-
offs in the predictive fit when using the reduced coefficient set, but overall the reduced
coefficient model fit is reasonable. The simplicity of the reduced model also helps in
understanding the importance of the five process parameters.
The coefficients given in Table X for flexural strength indicate that the amount of
filler, percent graphite, pull speed, and zone 2 temperature are important as are the
interaction between the filler - pull speed and the zone 2 temperature squared. For high
temperature short-beam shear strength, the amount of filler, the percentage of graphite, the
pull speed, and the zone 2 temperature are important as is the interaction between the
percent graphite - zone 2 temperature. Only the first zone of the die temperature does not
appear as an important first order term. Thus continued development of the pultrusion will
require further examination of all five process parameters with the exception of the first die
temperature heating zone. It is understandable that the process parameters of importance
for flexural strength (testing mainly fiber related properties) would be different than that for
short-beam shear strength (testing mainly resin matrix related properties).
29
-
SUMMARY
An experimental characterization of the pultrusion process has been conducted for
the composite material system of Shell EPON 9420/9470/537 epoxy with AS4-12K graphite.
The results indicate that four processing parameters are important in determining the
flexural and short-beam shear strength. These parameters are the amount of filler within
the resin, the percent of graphite fiber in the material, the pull speed, and the second die
temperature heating zone. The best mechanical properties are produced when the amount
of filler and graphite are held high and the pull speed is reduced. There are mixed results
for the effect of the second die temperature zone. A good experimental database has been
development for continued studies into more advanced pultrusion characterization.
30
-
REFERENCES
1. Statistical Design and Analysis of Experiments, Robert Mason, Richard Gunst, and JamesHess, John Wiley, 1989.
2. The Collected Works of George E.P. Box, Volume 1, edited by George C. Tiao,Wadsworth,1985
31
-
SECTION II
TWO-DIMENSIONAL FINITE ELEMENT MODELING OF
THE PULTRUSION OF FIBER/THERMOSETTING RESIN
COMPOSITE MATERIALS
-
I. INTRODUCTION
Composite materials used in the fabrication of
industrial products/components are under constant
development. Applications vary from widely sold consumer
products to high-performance aerospace components.
Important research areas include the design of composites,
performance optimization, and the prediction of composite
material behavior.
The pultrusion of thermosetting plastics is a prevalent
method for the manufacture of composite materials (Sumerak
and Martin, 1984). It is a continuous process having a high
potential for automation. It has the following potential
advantages over other fabrication methods:
"higher production rates
"less scrap
lower facility cost requirements
"lower direct labor cost requirements
lower secondary finishing operation costs
lower manufacturing cost
These are the reasons more and more material producers
and researchers have been attracted to study, develop, and
-
improve the method in recent years.
A typical pultrusion process is simply described in
Figure 1. Referring to the figure, the process requires a
creel system which contains continuous reinforcement
material, a resin tank which has a long gradual exit slope
to ensure good fiber impregnation, a preform die which
removes excess resin and forms the approximate desired cross
section shape, a cure die which is heated to the required
temperature to promote curing reaction, a pulling mechanism
which is responsible for moving the product continuously at
a constant speed, and a synchronized cut-off saw station
which automatically clamps and cuts the part to the desired
length.
0
-
3In appearance the pultrusion process is quite simple.
However, the interactive process variables are still not
understood clearly and thoroughly (Sumerak and Martin,
1984). The main factors which influence the production
capability and quality include the prescription of the
matrix, the die temperature profile, the pultrusion machine
speed (line speed), and the pulling force, with all except
the prescription of the matrix being adjustable machineparameters. To make up a proper and effective formulation
of resin requires in-depth chemical knowledge. It is
fortunate that there are resin supplies on the market which
satisfy different purposes (Shell Chemical Company, 1986).
In most situations the duty of a pultrusion operator is to
control the machine parameters. While machine parameters
are independently adjustable, they are interactive in thesense that they act together to influence the curing
characteristics of the material inside the die. It is well
recognized that the mechanical properties of the pultruded
composite material are affected directly by the degree-of-
cure (Batch and Macosko, 1987) . We know that the heat of
reaction, which is the measure of degree-of-cure, may be
expressed as a function of temperature. Temperature can be
called the driving force of pultrusion. A sufficient
degree-of-cure needs adequate reaction time, therefore it is
important to select an appropriate line speed in order to
ensure high quality. Thus precise control of the thermal
-
and chemical phenomena occurring within the die is of utmost
importance.
A wide variety of component shapes can be manufactured
through the pultrusion process. In this study only simple
profile shapes are treated, thus a two-dimensional heat
transfer model is applicable. Details of the formulation
and development focus directly upon the pultrusion of
thermosetting composite materials but the procedure and
techniques presented here are also valid for the modeling of
the pultrusion of thermoplastic composite materials. The
finite element method is widely recognized as the state-or-
the-art computational procedure for this class of problems
(Lewis et al., 1981; Burnett, 1987). A two-dimensional
finite element formulation capable of predicting the
temperature profile and the degree-of-cure of the material
is thus developed. Some numerical examples are also
presented. The solutions show that the work done lays a
good foundation for further study.
-
II. HEAT TRANSFER MODEL
A two-dimensional heat transfer model of the
thermosetting pultrusion process is formulated and a
numerical solution is developed using the finite element
method. Because another important aspect of the pultrusion
process, the degree-of-cure, is also a target of the study,
the heat of reaction is included in the heat transfer model.
The basic assumptions of the model are
the process is steady-state
the matrix and fiber have the same temperature at
any point in the die
the influence of pressure in the die on heat of
reaction can be neglected
for a rectangular cross section, the variation of
temperature along the width of die can be ignored
Based upon the above assumptions, the governing
differential equation of heat transfer can be expressed in
Cartesian coordinates thusly
ar a 6n\ a,, ai\~5r ~ ir^^r) ~ ir^^r)3x 3x dx dy y 9y
-
6where
T = temperature of the material
k = thermal conductivity of the material
c = heat capacity of the material
u = pultrusion line speed
HU = ultimate heat of reaction
mm = mass fraction of matrix
a = degree-of-cure
p = density of the material
The independent variables x and y denote longitudinal
and transverse directions, respectively. The rate of cure a
is a function of temperature and degree-of-cure, therefore
it is a function of position, thus satisfying the condition
of steady state.
During pultrusion the top heat platen and bottom heat
platen are controlled to be at same temperature, therefore
the boundary conditions can be expressed as follows in the
given coordinate system (refering to Figure 2)
T(0,y) = T0 (2a)
T(L,y) = TD(L) (2b)
T(x,|) = TD(x) (2c)
-
where
TQ = material temperature at the entrance of the die
TD = die interface temperature
L = length of die
d = thickness of the material in the die
d/2
x
Figure 2. Coordinates of Die with RectangularCross Section
The boundary equation, Eq. (2c), is symmetric about the
material mid-plane, y = 0, therefore we can assume that the
temperature and the degree-of-cure are distributed
symmetrically in the transverse direction. Considering the
condition of contact resistance, it is more appropriate to
change the temperature boundary condition to a convective
boundary condition. Thus Eq. (2c) is replaced by the
following condition
-
qy(x,|) = h[T(X,|) - TD(x)] (2d)
where
qn = outward-normal component of heat flux at the
boundary of y = d/2
h = die-material interface convection coefficient
The thermal properties of the material can be
approximated using the averaged values
P Pm Pf
c = mj(l - )ca + acj + (1 - mm)cf (4)
JL - ~ Vf + _ZL (5)^ [(l-a)k,, + akc] 1^
J_ = * " vf + ^ (6)
ky [(1-a)!^ + akc] k^
where the subscripts m and f refer to matrix and fiber,
respectively; u and c refer to uncured and cured matrix,
respectively; vf is the fiber volume fraction; kfx and kf are
the thermal conductivities of the fiber, the former in the
longitudinal direction and the latter in the transverse
direction. The matrix density pm depends on temperature and
degree-of-cure
-
p = 2 (7)ra 1 + 3e(T - T^ -
Y
In Eq. (7) , pQ is the matrix density at the temperature
of TQ, e is the thermal expansion coefficient of the matrix,
and y is the shrinkage coefficient of the matrix due to the
degree-of-cure. Thermal expansion of the fiber is ignored
since its expansion coefficient is much less than that of
the matrix.
From Eqs. (3) through (7), it is shown that all thermal
properties of the material are assumed to be continuous
functions of temperature and degree-of-cure. Therefore it
is not necessary to use different governing equations to fit
two or three different phase regions. This is convenient
for solution because some work to satisfy the continuity of
flux can be avoided.
For a die with a circular cross section, the
axisymmetric case will be considered. This is consistent
with the actual situation. At steady state the die
interface temperature can be thought of as not varying along
the direction of the circumference, therefore the assumption
of axisymmetric distribution of material temperature is
reasonable. Hence the heat transfer equation written in
cylindrical coordinates can be simplified as follows
3T 8 f. 3T\ 3- 3T,. 1, OT da f. /oxpcu (k) (k,) k - H pm = 0 ()V 9x dxv^8x' a r * * r^dr uH m 3t
-
10
where the subscript r represents the radial direction. The
expressions of boundary conditions and thermal properties of
the material are all similar to those in Cartesian
coordinates.
To avoid a singularity during numerical calculations we
rewrite Eq. (8) ,
3T 3 ,, 9TS 1 3 , , 3TX T, da /n\pcu --- (k ) --- (rk ) - H omm = 0 (?)v 3x ax^ax r d i ^ d i u ma
Then, multiplying Eq. (9) by r,
3T 8 , , 3T d , , 3T, TT da ~ /impcur --- (rk --- (rk, ) - H pm r = 0 (10)P
3x 3x ^3x 3r ^ dr uK m dt
Equation (10) is used to derive the formulation of the
finite element method in the study. A one-dimensional heat
transfer model is also treated, and the solution is compared
with that of the two-dimensional model. The governing
equation is from Hackett and Prasad (1989), with the heat of
reaction added (Erhun and Advani, 1990)
3T 2h/_, _ TT da n
In Eq. (11) , all thermal properties are determined using
Eqs. (3) through (7) . This is another point that is
different from the formulation of Hackett and Prasad (1989).
-
11
III. CURING PROCESS MODEL
It is recognized that the mechanical properties of a
thermosetting system depend strongly upon the crystalline
structure of the reactants, or in other terms, on the cure
of the matrix (Talbott and George, 1987). Curing
propagation within the die during pultrusion is a complex
chemical process which has not yet been clearly understood.
But some efforts have been made to unveil the relationships
among temperature, degree-of-cure, and rate-of-cure using
simplified descriptions of the cure chemistry in combination
with an appropriate cure model. In this study, formulas and
data relative to the curing process are principly taken from
Lee et al. (1982) and Lee and George (1987). The method
obtained therefrom is suitable for characterizing a matrix
containing catalysts. All the values and analytical
expressions in this reference are based on experiments with
Hercules 3501-6 resin.
The ultimate heat of reaction Hu is the amount of heat
generated by curing the material from the beginning of the
chemical reaction until the completion
-
12
where (dQ/dt)d is the instantaneous rate of heat generated
during the reaction and td is the amount of time required to
complete the reaction; the subscript d implies dynamic
scanning. The constant Hu is independent of the heating
rate. Lee et al . (1982) gives the value of the ultimate
heat of reaction, measured by the method of dynamic scanning
as
H,, = 473.6 5.4 J/g (13)
The rate-of-cure is a parameter that is assumed to be
proportional to the rate-of-heat of the thermosetting matrix
material
The degree-of-cure is defined as the integration of the
rate-of-cure (Lee et al., 1982)
t ta ~ I CH * ~ ni I ~d7 dt (15)
The value of a is always less than or equal to 1.
For convenient use in computer calculations, some
analytical expressions were derived by Lee et al. (1982) to
describe the rate-of-cure versus degree-of-cure and
temperature
-
13
= (k + k2a)(l - a)(B - a) , a s 0.3 (I6a)3t
= kjCl - a) , a > 0.3 (16b)dt
where
(17b)
k. = A3exp(-l) (17c)-3 "3 ^
RT
In Eqs. (17), Au A2, A3 are the pre-exponential
factors, AEir AE2, AE3 are the activation energies, R is the
universal gas constant, and T is the temperature measured by
the Kelvin scale; the values of these constants are listed
below
Aj = 2.101xl09 min"1 (18a)
A =-2.014xl09 min-1 (18b)
= 1.960xl05 min"1 (18c)
-
14
t = 8.07xl04 J/mol (19a)
= 7.78x104 J/mol (I9b)
R = 8.31441 J/g mol.K (20)
The constant B is independent of temperature and degree-of-
cure; its value may be selected as follows
B = 0.47 0.07 (21)
In this study, since only pultrusion at a steady state
is treated, time becomes the dependant variable. The speed
of matrix flow along the length of the die is assumed to be
equal to the line speed and the speed of matrix flow in .
other directions can be thought of as zero. Thus time is
only a function of x and the rate-of-cure can be rewritten
as follows
*5L = 3 (22)at ax
This formula will be used to replace it wherever it appears
later.
-
IV. FINITE ELEMENT FORMULATION
In this study, the Galerkin weighted residual method is
used to formulate the finite element method to solve the
heat transfer equation. The general form of the typical
element trial solution for temperature in Cartesian
coordinates, T(x,y), is
T(x,y) = Tj(t>j (x,y) (23)j=i
where n is the number of nodes in an element, T, is the
temperature at node j, and -(x,y) is the shape function.The residual of Eq. (1) is
T>, \ 9T 3 ,, 5T. 3 ,, 8T\ T, d&R(x
'y) -
pcu - **> ~ -
where uda/dx is the trial solution of the rate-of-cure which
has the same form as that of T
3d T-V ,-3a, , , x /o
-
16
//eR(x,y)(l)i(x)y)dxdy =
rrr ax a _ ar, a,, of ' ' d a . , . , . (26)JJ tpcu^7 ~ l^x^-) - ^-(ky^r) - Hupmmu J^dxdy >JJ* dx dx 8x dy y dy 3x= 0, i = 1, 2, .... n
where the subscript e implies integration over the domain of
the element.
From the "chain rule" of differentiation we have
a ' e n . a ar, , ,3x9^
3y 3y ' 3y ftt ' oy 5y>
Substituting Eqs. (27) into Eq. (26) yields
(27b)
5y
(28)
i = 1, 2, ..., n
The functions in the second integral in Eq. (28) are
perfectly dif ferentiable. Using the two-dimensional
divergence theorem, the integral can be reduced to a line
integration over the boundary of the element
-
17
(29)
where and are the direction cosines of the outwardx y
unit normal to the element boundary, and s is the natural
coordinate of the boundary.
The heat flux components in the x and y directions are
-
18
Figure 3. Notation for Interior Element BoundaryFlux Integral
-qnjds (32)
In Figure 3, (e) and (f) are adjacent elements; s and sare the routes of integration over the boundary of element
(e) and element (f), respectively; they are all
counterclockwise. The closed circuit integral of element (e)
can be written as
(33)
In Eq. (33), 1, 2, 3, and 4 represent the nodal numbers of
element (e). In the line integral on the right-hand side of
Eq. (33), for example, J,2 means integration along the route
from node 1 to node 2; the others follow this pattern.
Consider the line integral over the common boundary 2-3,
-
19
of heat flux and shape function, we have
= ~ (34a)
(34b)
and from Figure 3 , it is apparent that ds = -ds over segment
2-3. Thus the line integral over boundary 2-3 of element
(e) can be changed as follows
(35)
Using superposition, the total sum of the heat flux over the
internal boundary 2-3 is
2 3 (36)2 2 V '
3 3
From this example we determine that for interior
elements where all boundaries are internal, it is not
necessary to calculate the closed circuit integral.
Equation (28) is thus reduced to
(37)
dxdy , i = 1, 2, .... n
For exterior elements, only the line integral over the
external boundary makes a contribution. In this derivation
-
20
external boundary makes a contribution. In this derivation
the symmetric property of the system is used to reduce the
amount of computation. The boundary equations change to
T(0,y) = T0 (38a)
T(L,y) = TD(L) (38b)
,) = TD(x) (38c)
qy(x,|) = h[T(x,|) - TD(x)] (38d)
qy(x,0) = 0 (38e)
Note that
qn = h(T - TO) (39)
The integration is thus changed to
s (40)
where r is the external boundary over which the temperature
is unknown, and the heat flux qn is not equal to zero.
Substituting Eq. (40) into Eq. (28) and moving some terms
from the left-hand side of the equation to the right-hand
side yields
-
21
*3x i 3y
JhT^ds(41)
i = 1,2, ..., n
Substituting the trial function, Eq. (23) , into Eq. (37) and
Eq. (41) , we get
3. 3
-
22
where, for interior elements,
d). d
-
23
rj = 1
r, = -1
Figure 4. Element Local Coordinates
= d - Od - n) (49a)
in)
(49b)
(49c)
* ti) (49d)4
For an isoparametric element, the relationship between
the global coordinates and local coordinates has the same
form as the trial function
x = (50a)
-
24
=
E y/frjtf.T (50b)
where x.,y. are the global coordinates of the nodes of the
element. The coordinate transformation is determined by the
Jacobian matrix which-is given by
[J] =
ax3
Jx
ay'as
dy_
Jll J12
/21 J22.
(51)
Note that in Eqs. (50), x and y are functions of 0.. In
order to obtain the elements of the Jacobian matrix we first
have to know the derivatives of the shape functions 0-(,rj).They are easily obtained from Eqs. (49) .
4), i
= -1(1 -4
(52a)
at] (52b)
4(52c)
J)^ 1 5d>. i= -1(1 + i,) , -^ = 1(1 -$ 4 at) 4 (52d)
Thus the elements of the Jacobian matrix can be written as
follows
-
25
.
Jn = E xj~j=i "4(x3-x4)(l+T1)] (53a)
r V> 0(J>J lrf12 = E y^ = 7[ (53b)
J2i = E x,~ = TK^4-xiXl-W + (Xa-XaXUj=l "I 4
(53c)
5(1). iJ22 = E li = 7[Cy4-oti 4j=i (y3-y2)(l + 0] (53d)
Using the "chain rule" of differentiation we have
ay (54a)
3y>j oy (54b)
which can be written in matrix form as
dy
3y]
= [J]34,.ax (55)
Inverting Eq. (55) yields
3x (56)
3yJ
-
26
where
PT1 = ^ 7
dy_
(57)
and |J| is the determinant of the Jacobian matrix, which canbe written as
III - -fy- - dx 3y1 ' ~ " -
(58)
It is well known that after coordinate transformation the
infinitesimal area element becomes
dA = dxdy = |J|ddti (59)Equations (45) and (46) can now be rewritten in terms of
local coordinates as
>. 3cJ).*dy
i i
, = // H^ m^ l^
(60a)
(60b)-1-1
For the exterior elements, referring to Figure 4,
assuming that segment 3-4 is an external boundary, rj = 1 onboundary 3-4; substituting r? = 1 into the shape function
expressions we then obtain
(61a)
-
27
4)4* = d - Od + 1) = d - 0 (6lc)
where 0* refers to shape functions on the boundary. In
order to obtain the value of the line integral we need to
derive the differential arc length ds
ds = \/dx2 + dy2 = ^ 3x
i + 4 ^ = |/(^ - ^ )2 + '(y3 - yf ft = ~3* + T^l (63)
then we can obtain
i/^ T^ ds = /h(TD34); + TD4
-
28
i i
y dy dy
(66a)
and
1 l l
4>l + IV *,*)(!> Idf (66b)-1-1 -i
In Eqs. (66), for generality, we replace subscripts 3
and 4 with k and , respectively.
In the computer program we use bilinear Gauss-Legendre
quadrature formulas to obtain the values of Eqs. (60) and
Eqs. (66) . The formulas for k^- and F- become
m m 3d). 3d). 636. m) IJ|](EO,V - Et* K o=l
-
29
m m7i = EEi /_v z_/0=1 p=i p^) (68b)E frCV;0 = 1
where WQ and W are the weighting coefficients and o and rjare the Gauss-point coordinates. In the computations we use
a 2 x 2 Gauss quadrature; that is to say, m = 2, thus
w0- wp =
v/3=
(69a)
(69b)
In Eqs. (60), (66), (67), and (68), d
-
30
T(0,r) = T0 (70a)
T(L,r) = T0(L) (70b)
T(xJo) = TD(x) (70c)
= h[r(x,ro) - TD(x)] (70d)
qr(x,0) = 0 (70e)
where ro is the internal radius of the die. The element
trial solution for temperature is
T(x,r) = T j y r ) (71)
Using Eq. (10), the weighted residual equation at node
i in an annular element (referring to Figure 5) is
r fj L' Oft OT\ O y 1 Ol\[pcur- - (rk -) - (rk,)> d x . d x . d x . dr dr
(72)
-mtu]4)j27idrdx = 0 , i = 1, 2, ..., ndxIn Eq. (72) , the common factor 2ir can be cancelled,
through integration by parts we obtain
a ,, 5 T X . . . /* r , 3T ^jdrdx = / / rk drdx - 4> rkx4>jH ds v/:>
-
31
_ f ( _l(rk *L)4> .drdx- = f f rk -^-^idrdx - rk^cj, .n ds (73b)JJeSr r 3r ' JJe rar or J ^ or ' r
i = 1 , 2 , . . . , n
Substituting Eqs. (73) into the weighted residual equation
and using boundary conditions to simplify the resulting
expression, we obtain
ar , arai afa^
= 0
i = 1, 2, , ..., n
Then, substituting Eq. (71) into Eq. (74) , expanding the
resulting expression, and writing it in matrix form we have
where k( . and F. for interior elements and exterior elements
are given respectively as
,_, x(76a)
F. = ff H . p n v u r i d r d x (76b)J J e cC5
and
-
32
kj. = //Oy-- + krr i + pcunjK^)drdx
hr j(J) -ds
(77b)
For a linear isoparametric quadrilateral element the
geometric functions are
(78a)
where the 0j are exactly the same as in Eqs. (49).Expressing Eqs. (76) and Eqs. (77) in terms of local
coordinates and applying the bilinear Guass-Legendre
quadrature formulas, the final equations which can be used
directly in the computer program are obtained and given by
-i ^-i VA ^A. wi t_aO i p * (79a)
Vy W W [ H p m ur
-
33
0=1 p=l
(80a)
2 2
0=1
F. = W W [H pm ur 4>-|J|]o pl u" m -v T,| U(0=1 p=l
2
+ E0=1
(80b)
where Eqs. (79) apply to interior elements and Eqs. (80)
apply to exterior elements. .In the equations, all indices
have the same definitions as they were assigned relative to
the Cartesian coordinates, except where r is used instead of
y. Substituting Eqs. (79) or Eqs. (80) into Eq.(44),
element heat transfer equations for an axisymetric condition
will be formed.
The finite element method formulation for a one-
dimensional heat transfer model is shown below. The
equations are refined from Hackett and Prasad (1989). The
element residual equations are
(81)FJwhere
-
34
pcu 2hL(e)
L(e) 2 3d
(82a)2 3d
(82b)
(82c)
(82d)
L(e) 2 3d
2 3d
p - F - + " (83)
In the above equations, all material properties and rates-
of-cure are functions of position but are treated as being
constant within each element.
-
35
V. FORMULATION OF THE DEGREE-OF-CURE MODEL
AND CALCULATION TECHNIQUE
In this study we use numerical integration to obtain
the degree-of-cure solution. Beginning at the die entrance,
the degree-of-cure in the. transverse direction is set to
zero, that is
a(0,y) = 0 (84)
From Eq. (17) through Eq. (21) we can obtain the rate-
of-cure da/dt through the temperature profile. Then, using
Eq. (22) we can change rate-of-cure from the form of
derivative with respect to time to the form of derivative
with respect to the variable x
0*. = I.^. (85)ax u a
Then a stepping procedure is used to integrate the
gradient to find a further into the die
a(x + dx,y) = a(x,y) + -[^ r(x,y) + -^ -(x + dx,y)]dx (86)2 dx dx
Using the mesh of the finite element method, Eq. (86)
may be rewritten as follows
-
36
o(x. + L>>,y) = a(xi>yi) + ^(^ ^
2 ax(87)
where i is the nodal number. The profile for the degree-of-
cure is determined through Eq. (87).
From the governing differential equation of heat
transfer it is easily seen that temperature and degree-of-
cure are coupled. We use the method of iteration to solve
this problem. At first we set the degree-of-cure equal to
zero everywhere. Thus it is not difficult to obtain the
solution which will serve as the initial value. Depending
on that value, the iteration will be developed successfully.
The iteration procedure may be simply expressed as
1. Let a(1) = 0 to obtain T(1>.
2. From T(1) obtain da(2)/dt and a
-
VI. NUMERICAL SOLUTION AND DISCUSSION
Three typical sets of die temperature profiles combined
with three different line speeds are considered, using the
finite element formulation derived in the previous
rectangular and circular, are treated. All solutions of the
above eighteen cases are satisfactory.
First, it should be pointed out that due to a lack of
data, we use a temperature profile of the die interface,
which was obtained with no material flow through the die, as
the boundary condition. During pultrusion, the material
near the die entrance will extract heat from the die and
over the remainder of the die the material will release heat
to the die. So, the actual temperature profile of the die
interface during pultrusion may be somewhat different from
that used in the paper. The error will be small because of
the poor thermal conductivity of the composite material and
it will not influence the general shape of the profile and
the qualitative analysis. Comparing the temperature profile
of the material with that of die interface, we can find some
rule of temperature distribution. Over the beginning part
of the die, the temperature of the die interface is higher
37
-
38
than that of the composite, the die providing heat to the
material during the curing reaction. The length of this
region depends on the line speed primarily; the higher the
line speed, the longer is this region. Over the remainder
of die, the temperature of the material is higher than that
of the die interface due to the accumulation of heat of
reaction. The die draws heat from the curing material,
thereby reducing the thermal shock to the product upon its
exit from the die.
300
DIE TEMP. SET 370 DEGREE F (AXISYM.)UNE SPEED: 14 INCH/MIN.
0250-
*-~t
8 200-oH150
*-H
B
so H
10 20 30 40 50 60 70DISTANCE FROM DDE ENTOANCB (CM)
C.T.
B.T.
90 100
Figure 6. Temperature Profile of the Material
-
39
From Figure 6 we see that the centerline temperature of
the composite is distinctly lower than the boundary
temperature near the entrance of the die, even though the
radius is less than 1 centimeter. The difference will be
greater with increasing radius or thickness. This
phenomenon explains the necessity of controlling a gentle
gradient of die temperature near the entrance, otherwise a
cured matrix skin may be formed on the die wall and a very
poor product surface will result.
DIE TEMP. SET 400 DEGREE F (AXISYM)SPEED: 8 INCH/MIR
300
10 30 40 50 60 70DISTANCE FROM DIE ENTRANCE (CM)
80 90 100
Figure 7. Temperature Profile Solved with ConvectiveBoundary Conditions
-
40
The resulting material temperature profiles are
obtained with temperature boundary conditions. Because the
material in the die undergoes three different phases:
liquid, gel, and solid, the value of the die-material
interface convection coefficient is difficult to determine.
This is an obstacle to applying convective boundary
conditions. As examples, we calculate two cases with the
coefficient h held constant over the whole domain of the
die. We find that when h = 0.1, the solution is almost
identical to the solution obtained with temperature boundary
conditions. Another solution, with h = 1, is also very
close to the solution obtained with temperature boundary
conditions. This seems to indicate that within certain
ranges, the variation of the convection coefficient does not
greatly influence the temperature profile of the material
From Figures 6 and 7, curve oscillations can be noted. This
is caused by the convective term in the heat transfer
equation. This term makes k.. not equal to k-- in the matrix
[K]; that is to say, it makes the operator not self-adjoint(Zienkiewicz and Taylor, 1989). But if we adjust theboundary conditions properly, the numerical oscillations
will be improved greatly. From analysis of the
distribution of material temperature in the die, we know
that the material temperature should be higher than the die
temperature at the exit of the die. Therefore we change Eq.
(2b) from a constant to a linear function of y and assume
-
41
that the centerline temperature is 8 C higher than the die
temperature. The new results are shown in Figure 8.
300
5250-I
0200-
150-
I100-
50-
Dffi TEMP. SET 370 DEGREE F (AXBYE)IJNE SPEED: 14 INCH/MIR
C.T.
B.T.
10 20 30 40 50 60 70 80 90 100DISTANCE FROM DIE ENTRANCE (CM)
Figure 8. Temperature Profile Solved with AdjustedBoundary Conditions
Comparing the curve of degree-of-cure with a different
line speed but with the same die temperature we find that
when the line speed increases, the final degree-of-cure (the
degree-of-cure at the die exit) decreases. In some cases
the final degree-of-cure is too low to yield -a qualified
product. If a higher die temperature set is used, it is
-
42
possible to obtain a sufficiently cured composite material
with a high line speed. This phenomenon shows that it is
important to select an appropriate combination of die
temperature set and line speed in order to produce a high
quality as well as a high quantity of composite components.
It should be explained that in the usual situation, the
prescription of resin includes curing agent, curing agent
1.00DIE TEMP. SET 370 DEGREE F
10 20 30 40 50 60 70DISTANCE FROM DE ENTRANCE (CM)
80 90 100
Figure 9. Profile of the Degree-of-Cure of the Material
accelerator, and the resin itself. But in this paper the
curing process model is only based on the Hercules 3501-6
-
43
resin. So, in an actual pultrusion process, the speed-of-
cure reaction will be faster and a high'er line speed will be
allowable. There are also other techniques for increasing
the degree-of-cure of pultruded material, such as pre-
heating before the material enters the die and post-heating
after the material leaves the die. The details of these
techniques are beyond the topic of this paper.
According to Batch and Macosko (1987), when the degree-
of-cure is between 0.01 and 0.3, the matrix changes into the
gel phase. Observing the degree-of-cure profile we see that
the gel region in the die is located between 20 cm to 40 cm
from the die entrance (relative to a 36-inch length die).
Thus we can roughly divide the die into three regions: the
first one-third of the die is the liquid region, the next
one-sixth of the die is the gel region, and the last part of
the die is the solid region. The position of peak exotherm
of the material is usually located at the beginning of solid
region. The relative positions of the sub-regions and the
magnitude of material temperature may be varied based upon
different prescriptions of resin and techniques utilized in
processing, but the general rule of distribution is: in the
liquid region, the temperature of the material is lower
than that of the die and its average slop is gentle; in the
gel region, the material temperature rapidly rises from
lower than the die temperature to higher than the die
temperature and its gradient is relatively sharp; in the
-
44
solid region, the material temperature is higher than that
of the die and its average slope is gentle.
We know that the resin pressure model is another
important sub-model of the pultrusion process. If a problem
concerned with the resin pressure model is to be solved, the
viscosity of the resin along the die must first be known.
If the profile of the material temperature has been
obtained, it is easy to determine the viscosity using the
formula given by Lee et al. (1982),
H = n.expdJ/RT + Kcc) , a
-
45
temperature profile as well as with the bulk degree-of-cure
profile obtained with the two-dimensional model.
DIE TEMP. SET 400 DEGREE F (AXKM)UNE SPEED: 8 INCH/MIN.
10 20 30 40 50 60 70DISTANCE ITOM DIE ENTRANCE (CM)
80 90 100
Figure 10. Temperature Profile of the One-Dimensional Model
We find that the differences between the results
obtained with the one-dimensional model and those obtained
with the two-dimensional model are very slight. If one is
not interested in the variation of temperature and degree-
of-cure in the direction of thickness, using the one-
dimensional model is recommended since it is more
convenient.
-
46
REFERENCES
Batch, G.L. and C.W. Macosko, 1987. "A Computer Analysis of
Temperature and Pressure Distributions in a Pultrusion
Die," 42nd Annual Conference, Composites Institute, The
Society of the Plastics Industry, Inc.
Burnett, D.S. 1987. Finite Element Analysis. Addison-Wesley
Publishing Company.
Erhun, M. and S.G. Advani, 1990. "A Predictive Model for
Heat Flow During Crystallization of Semi-Crystalline
Polymers," Journal of Thermoplastic Composite
Materials. 3: 90-109.
Hackett, R.M. and S.N. Prasad, 1989. "Pultrusion Process
Modeling," Advances in Thermoplastic Matrix Composite
Materials. American Society for Testing and Material,
62-70.
Lee, W.I.,C.L. Alfred and S.S. George, 1982. "Heat of
Reaction, Degree of Cure, and Viscosity of Hercules
3501-6 Resin," Journal of Composite Materials. 16:
510-520.
Lee, W.I. and S.S. George, 1987. "A Model of the
Manufacturing Process of Thermoplastic Matrix
Composites," Journal of Composite Materials, 21: 1017-
1055.
-
47
Lewis, R.W., K. Morgan and O.C. Zienkiewicz, 1981. Numerical
Methods in Heat Transfer. John Wiley & Sons Ltd.
Shell Chemical Company, 1986. "Pultrusion with EPON Epoxy
Resin," Technical Bulletin.
Sumerak, J. and J. Martin, 1984. "Pultrusion Process
Variables and Their Effective upon Manufacturing
Capability," 39th Annual SPI Conference.
Talbott, M.F. and S.S. George, 1987. "The Effects of
Crystallinity on the Mechanical Properties of Peek
Polymer and Graphite Fiber Reinforced Peek," Journal of
Composite Materials, 21: 1056-1081
Zienkiewicz, O.C. and R.L. Taylor, 1989. The Finite Element
Method (Fourth Edition). Mcgraw-Hill Book Company (UK)
Limited.
-
APPENDIX
-
W300
05?250
wo 200-
0H0
-
50
W. SET 370 DEGREE OF FUNE $EED. 2 m/m
10 20 30 40 50 60 70 80 90 100DOTCE M DIE EMH4NCE (CM)
BULK DEGREE Of CURE
Figure A-2
-
51
a 300I0I 250 H
BU 200-0B
0BQB100-
J 5 0 H
0
D. SET 370 DEGREE OF FUNE spEEft 8 m\jm
I T I i r i10 20 30 40 50 60 70 80 90 100
DISTANCE MDEENHUNCE (CM)
C.T. B.T.
Figure A-3
-
52
1.00
0.90-
0.80-
W 0 . 7 0 -
00.60-fe0.50-jH0.40^9Q0.30-J
0.20
0.1(Ho.oo-
DIE TEMP. SET 370 DEGREE OF F
0 10 20 30 40 50 60 70DEIM FROM DIB ENTOANCE (CM)
90 100
BULK DEGREE Of CURE
Figure A-4
-
53
w300
0250-
200-w0facH1500WQK100-
H2
DIE TEMP. SET 370 DEGREE OF FUNE SPEED: 14
i i i i10 20 50 40 50 60 70 80 90 100
DISTANCE FRQU DIB ENHANCE (CM)
C.T. B.I.
Figure A-5
-
1.00
0.90-
0.80-
pj '70"00.60-fc0 0.50 -
H
900.30-
0.20-
0.10-
0.00
P. SET 370 DEGREE OF FLINE SPEED: 14 M/M.
0 10 20 30 40 50 60 70 80 90 100DET FROU DIE ENCE (CM)
BULK DEGREE OF CURE
Figure A-6
-
55
W3009K01250 -^
200-fcoH
0wQH100-
0
HP. SET 400 DEGREE OF FUNE S^CED. 2 DO/MM
I I I0 10 20 30 40 50 60 70
DISTANCE TCOM DIE BMCE (CM)80 90 100
CT. B.T.
Figure A-7
-
56
1.00
0.90
0.80-
W 0 . 7 0 -
00.60-(n0
0.501wwS 0.40^0Q 0.30 -
0.20-
0.10-
0.00
DIE TEMP. SET 400 DEGREE OF F2 INCH/MR
0 10 20 30 40 50 60 70 80 90 100BBr FROM DIE EMANCE (CM)
RAX DEGREE OF CURE
Figure A-8
-
57
"3002w
250-
w0200
g1SO0W 'Q
50-W
I o0
DIE TEMP. SET 400 DEGREE OF FUNE SPEED-. 8 INCH/MM
I T T I I
10 20 30 40 50 60 70 80 30 100DOTE FROM DIB ENTRANCE (CM)
CT. --B.T.
Figure A-9
-
58
DIE TEMP. SET 400 DEGREE OF FUNE spffl>. a m/m
30 40 50 60 70DOTE m)M DIE MANGE (CM)
80 90 100
BULK DEGREE OF CURE
Figure A-10
-
59
W300
K0I 250
W0fao
200-
H1500WQ
* 5
-
60
1.00
0.90-
0.80-
W0.70-
00.60-
0.5(H.H0.40-0wQ 0.30 -
0.20-
0.10-
0.00
DIE TEMP. SET 400 DEGREE OF FUNE SPEED: 14 1NCH/UIN.
0 10 20 30 40 50 60 70DIB ENTRANCE (CM)
80 90 100
BULK DEGREE Of CURE
Figure A-12
-
61
W300
0,25(H
200-8faoB1500w
2e o
DIE TEMP. SET 430 DEGREUNE SPEE& 2 m/m OF F
0 10 20 30 40 50 60 70DISTANCE fROU DIB EM1UNCE (CU)
80 90 100
CT. B.T.
Figure A-13
-
62
DIE TEMP. SET 430 OF F
10 20 30 40 50 60 70 80 90 100DISTANCE FHOU DIE ENTRANCE (CM)
BULK DEGREE Of CURE
Figure A-14
-
63
H300
DIE TEMP. SET 430 DEGREE OF FUNE SPEED: 8 INCH/MM
10 20 30 40 50 60 70 80 90 100DISTANCE fROU DIE EMWE (CM)
C.T. --B.T.
Figure A-15
-
64
IMP. SET 430 DEGREE OF F
1.00
0.90-
0.80-
W 0 . 7 0 -K00.601fc0
0.501HK 0.4010H00.301
0.20-
0.10-
0.000 10 20 30 40 50 60 70
DISTANCE YSM DIE ENMCE (CM)90 100
BULK DEGREE OF CURE
Figure A-16
-
65
H300
K0.1.250
B0fe0
200-
H1500HQW 1 0 0K
i 5 0H
DIE TEMP. SET 430 DEGREE OF FIINE SPEED: 14 INCH/IN.
10 20 30 40 50 60 70DISTANCE FROM DIE EMANCE (CM)
80 90 100
C.T.B.T.
Figure A-17
-
66
DIE TEMP. SET 430 DEGREE OF FUNE SPEED: 14 INCH/ME
10 20 30 40 50 60 70 80 90 100DISTANCE FROM DIE ENTRANCE (CM)
BULK DEGREE OF CURE
Figure A-18
-
67
H300
030250-
W0 200-
w1500wQH100-
0
DIE TEMP. SET 370 DEGREE OF F (AXBffl)UNE SPEED: 2 INCH/MIR
I I I I I I I I0 10 20 30 40 50 60 70
DISTANCE Mi DIE EMMCE (CM)80 90 100
C.T.B.T.
Figure A-19
-
68
1.00
0.90-
0.80-
B0.70-
00.60-1fc0
0.50-]H0.4010P0.30-
0.20-
0.10-
0.00
TEMP. SET 370 DEGREE OF F (AXBYlt)UNE SPEED. 2 INCH/iR
0 10 20 30 40 50 60 70 80 90 100DISTANCE FROU DIE EMCE (CM)
BULK DEGREE OF CURE
Figure A-20
-
69
H300
DIE TEMP. SET 370 DEGREE OF F AXISYM.UNE SPEED: 8 INCH/MM
0 10 20 30 40 50 60 70DISTANCE fflOU DIE ENCE (CM)
80 90 100
C.T. B.T.
Figure A-21
-
70
.00
0.90-
0.80-
H0.70-
00.60-
0 0.50 -
H0.40-0Q0.30-
0.20-
0,10-
o.oo-
TEMP. SET 370 DEGREE OF F (AXBYtt)HE SPEED: 8 INCH/MM
0 10 20 30 40 50 60 70 80 90 100DOTCE FROM DIE EMCE (CM)
BULK DEGREE OF CURE
Figure A-22
-
71
W 3 0 0
CTT Q^fl nPPOTT? fW 1? f AYTQVMOLl 0/U UEjliKijIj Uf r (AAlolM.UNE SPEED: 14 INCH/MM
10 20 30 40 50 60 70 80 90 100DISTANCE MM DIE EMMCE (CM)
C.T. B.T.
Figure A-23
-
72
.00
0.90-
0.80 -
W 0.701
00.60-)fc0 0.501
wK 0.4010HP 0.301
0.20-
0 , 1 0 -
0.00
IP. SET 370 DEGREE OF F (AXISYM,UNE SPEED: 14 INCH/MM
0 10 20 30 40 50 60 70 80 90 100DISTANCE FROM DIE EMEANCE (CM)
BULK DEGREE OF CURE
Figure A-24
-
73
DIE TEMP. SET 400 DEGREE OF F (AM)UNE SPEED: 2 INCH/MM
10 20 30 40 50 60 70 80 90 100DISTANCE mm DIE ENTRANCE (CM)
C.T.B.T.
Figure A-25
-
74
1.00
0.90 -I
0.8'
gO,7(H00,60^fc0 0.501
w(3E 0.40^0HP 0.30 -I
0.20-
0,10-
0,000
MR SET 400 DEGREE OF F (AHSYH.)UNE SPEED: 2 INCH/MM
i r \ r10 20 30 40
DISTANCE FROM DIE ENTRANCE (CM)
BULK DEGREE OF CURE
Figure A-26
-
75
DE TEMP. SET 400 DEGREE OF F (AXISYM.UNE SPEED: 8 INCH/MM
H300
10 20 30 40 50 60 70 80 90 100DISTANCE M Dffi EMCE (CM)
C.T. B.T.
Figure A-27
-
76
DIE TEMP. SET 400 DEGREE OF F (AXISYM.)UNE SPEED: 8 INCH/MIR
i \ 1 1 1 r10 20 30 40 50 60 70 80 90 100
DISTANCE FROM DIE ENWNCE (CM)
BULK DEGREE OF CURE
Figure A-2 8
-
77
H300
0250-
B0 200-oH1500
H100K
0
DE TEMP. SET 400 DEGREE OF F (AXISYM.)UNE SPEED: 14 iCH/MIN.
10 20 30 40 50 60 70 80 90 100DISTANCE FfflU DIE EMANCE (CM)
C.T. B.T.
Figure A-29
-
78
1.00
0.90-
0.80-
00.601fc0
0.501HK 0.40-10HP 0.301
0.20-
0.10-
0.000
DIE TEMP. SET 400 DEGREE OF F (AXBYEUNE SPEED: 14 INCH/ME
20 30 40 50 60" 70DISTANCE FROM DIE EMRANCE (CM)
80 90 100
BULK DEGREE OF CURE
Figure A-30
-
79
H300
0250^
200-H0fc0H1500HPH l O O H
0.
0
DIE TEMP. SET 430 DEGREE OF F (AXBYlt)UNE SPEED: 2 INCH/MM
i r i r10 20 50 40 50 60 70 80 90 100
DISTANCE fHOU DIE EMANCE (CM)
C.T.--B.T.
Figure A-31
-
80
DIE TEMP, SET 430 DEGREE OF F (AXBffl)HE SPEED: 2 INCH/MM
10 20 30 40 50 60 70mm m DIE EMNCE (CM) 80 90 100
BULK DEGREE OF CURE
Figure A-32
-
81
H300
K0
250-
200-H0fc0H1500wQH100-
o
fP. SET 430 DEGREE OF F (AXBYtt)UNE SPEED: 8 INCH/lflR
i i i i r r0 10 20 50 40 50 60 70
DISTANCE FROM DIE EMANCE (CM)80 90 100
C.T. B.T.
Figure A-33
-
82
~r10
TEMP. SET 430 DEGREE OF F (AXISYM.)IJNE SPEED 8 INCH/MM
30 40 50 60 70DISTANCE fflOU DIE ENIKANCE (CM)
80 90 100
BULK DEGREE OF CURE
Figure A-34
-
83
W300
TEMP. SET 430 DEGREE OF F (AXISYM.)UNESPEEft 14 INCH/ME
10 20 30 40 50 60 70DISTANCE Mi DIE EMMCE (CM)
80 90 100
C.T. BJ.
Figure A-35
-
84
1.00
0.90-
0.80-
gOJ(H00 .60H
DE TIP. SET 430[JNE SPEED: 14
OF F (AXISYM.)
30 40 50 60 70DISTANCE FROM DIE ENWNCE (CM)
80 90 100
BULK DEGREE OF CURE
Figure A-36
-
NASA- .
S-.-.v* .'.j- - ;Report Documentation Page
1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.
4. Title and Subtitle
Pultrusion Process Characterization
5. Report Date
September 25, 19916. Performing Organization Code
I 7. Authorls)James G. VaughanRobert M. Hackett
9. Performing Organization Name and Address
School of Engineeringj The University of Mississippi
University, MS 3867712. Sponsoring Agency Name and AddressNational Aeronautics and Space AdministrationMarshall Space Flight Center, AL 35812
8. Performing Organization Report No.
10. Work Unit No.
11. Contract or Grant No.
NAS8-3719313. Type of Report and Period Covered
Final7 Aug. 9 0 - 6 Aug..91
14. Sponsoring Agency Code
15. Supplementary Notes
16. Abstract
; 17. Key Words (Suggested by Author(sl)I Pultrusion, Modeling, Finite Element,'. Characterization
18. Distribution Statement
19. Security Classif. (of this report)Unclassif ied
20. Security Classif. (of this page)Unclassified
21. No. of pages I 22. Price
NASA FORM 1626 OCT 86